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dc.contributor.authorBallesteros, A.-
dc.contributor.authorMarrero, J. C.-
dc.contributor.authorRavanpak, Z.-
dc.identifierdoi: 10.1088/1751-8121/aa617b-
dc.identifierissn: 1751-8121-
dc.identifier.citationJournal of Physics A: Mathematical and Theoretical 50: 145204 (2017)-
dc.description25 pags., 1 fig.-
dc.description.abstractGiven a LiePoisson completely integrable bi-Hamiltonian system on ℝ, we present a method which allows us to construct, under certain conditions, a completely integrable bi-Hamiltonian deformation of the initial LiePoisson system on a non-abelian PoissonLie group G of dimension n, where n ∈ ℝ is the deformation parameter. Moreover, we show that from the two multiplicative (PoissonLie) Hamiltonian structures on G- that underly the dynamics of the deformed system and by making use of the group law on G, one may obtain two completely integrable Hamiltonian systems on G×G By construction, both systems admit reduction, via the multiplication in G, to the deformed bi-Hamiltonian system in G. The previous approach is applied to two relevant LiePoisson completely integrable bi-Hamiltonian systems: the Lorenz and Euler top systems.-
dc.description.sponsorshipAB has been partially supported by Ministerio de Economía y Competitividad (MINECO, Spain) under grants MTM2013-43820-P and MTM2016-79639-P (AEI/FEDER, UE), and by Junta de Castilla y León (Spain) under grants BU278U14 and VA057U16. JCM has been partially supported by Ministerio de Economía y Competitividad (MINECO, Spain) under grant MTM 2015-64166-C2-2-P. ZR has been partially supported by Ministry of Science Research and Technology (MSRT, Iran) under grant 2015-215401-
dc.publisherInstitute of Physics Publishing-
dc.relationMINECO/ICTI2013-2016/ MTM2015-64166-C2-2-P-
dc.subjectLie–Poisson structures-
dc.subjectIntegrable deformations, coalgebras-
dc.subjectCompletely integrable systems-
dc.subjectBi-Hamiltonian systems-
dc.subjectHamiltonian systems-
dc.subjectPoisson–Lie groups-
dc.titlePoisson-Lie groups, bi-Hamiltonian systems and integrable deformations-
dc.description.versionPeer Reviewed-
dc.contributor.funderMinistry of Science, Research, and Technology (Iran)-
dc.contributor.funderJunta de Castilla y León-
dc.contributor.funderMinisterio de Economía y Competitividad (España)-
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